How to do texture box mapping with blending in Blender Internal
The key to this is in the node set up in the first image, the image texture node. It uses "box" projection, with the blend is set to 1.000. This was a feature added specifically for the purpose of blending the image being projected from all directions (even if that image is the same texture). 
The description provided in the blender 2.79 manual is here:
https://docs.blender.org/manual/en/latest/render/cycles/nodes/types/textures/image.html

Projection
Projection to use for mapping the textures.

Box
Maps the image to the six sides of a virtual box, based on the normal, using XY, YZ and XYZ coordinates depending on the side.

Blend
For Box mapping, the amount to blend between sides of the box, to get rid of sharp transitions between the different sides. Blending is useful to map a procedural-like image texture pattern seamlessly on a model. 0.0 gives no blending; higher values give a smoother transition.